The mean deviation of the data 2, 9, 9, 3, 6, 9, 4 from the mean is :
A. `(42)/(7)`
B. `(18)/(7)`
C. `2.5`
D. `(50)/(7)`

Options

A. B
B. D
C. C
D. A

Answer

To find the mean deviation of the data set \(2, 9, 9, 3, 6, 9, 4\) from the mean, we will follow these steps:

### Step 1: Calculate the Mean
First, we need to calculate the mean of the given data.

\[ \text{Mean} ( \bar{x} ) = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]

Calculating the sum:

\[ 2 + 9 + 9 + 3 + 6 + 9 + 4 = 42 \]

The number of observations is \(7\).

Now, we can find the mean:

\[ \bar{x} = \frac{42}{7} = 6 \]

### Step 2: Calculate the Mean Deviation
The formula for mean deviation (MD) is:

\[ MD = \frac{1}{n} \sum |x_i - \bar{x}| \]

Where \(n\) is the number of observations, \(x_i\) are the individual observations, and \(\bar{x}\) is the mean.

Substituting the values we have:

\[ MD = \frac{1}{7} \sum |x_i - 6| \]

Now, we will calculate \( |x_i - 6| \) for each observation:

- For \(2\): \( |2 - 6| = 4 \)
- For \(9\): \( |9 - 6| = 3 \)
- For \(9\): \( |9 - 6| = 3 \)
- For \(3\): \( |3 - 6| = 3 \)
- For \(6\): \( |6 - 6| = 0 \)
- For \(9\): \( |9 - 6| = 3 \)
- For \(4\): \( |4 - 6| = 2 \)

Now we sum these absolute deviations:

\[ 4 + 3 + 3 + 3 + 0 + 3 + 2 = 18 \]

Now, substituting back into the mean deviation formula:

\[ MD = \frac{1}{7} \times 18 = \frac{18}{7} \]

### Final Answer
Thus, the mean deviation of the data from the mean is:

\[ \frac{18}{7} \]

### Conclusion
The correct option is **B. \( \frac{18}{7} \)**.

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